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SPECIFICATION TESTS FOR LATTICE PROCESSES

  • Javier Hidalgo (a1) and Myung Hwan Seo (a1)
Abstract

We consider an omnibus test for the correct specification of the dynamics of a sequence $\left\{ {x\left( t \right)} \right\}_{t \in Z^d } $ in a lattice. As it happens with causal models and d = 1, its asymptotic distribution is not pivotal and depends on the estimator of the unknown parameters of the model under the null hypothesis. One first main goal of the paper is to provide a transformation to obtain an asymptotic distribution that is free of nuisance parameters. Secondly, we propose a bootstrap analog of the transformation and show its validity. Thirdly, we discuss the results when $\left\{ {x\left( t \right)} \right\}_{t \in Z^d } $ are the errors of a parametric regression model. As a by product, we also discuss the asymptotic normality of the least squares estimator of the parameters of the regression model under very mild conditions. Finally, we present a small Monte Carlo experiment to shed some light on the finite sample behavior of our test.

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Corresponding author
*Address correspondence to Myung Hwan Seo, London School of Economics, Houghton St., London WC2A 2AE, UK; e-mail: m.seo@lse.ac.uk.; or to: Seoul National University, Kwan-Ak Gu, Seoul, Korea.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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